As Beijing takes on its heavily indebted private companies, China’s HNA Group Co. is quietly getting a helping hand.

Last week, Chinese authorities seized Anbang Insurance Group Co., a conglomerate that had been buying assets around the world. Yet behind the scenes the Chinese government has been aiding HNA, a similarly acquisitive giant with growing financial troubles. Some officials in Beijing, for instance, have encouraged state-owned banks to keep lending to HNA, people familiar with the matter say.